It reopened to the public at the weekend, and the tweaks are so subtle that it may be difficult to see just what’s been improved. That’s no bad thing. It may actually, in an age of museum overexpansion, be a statement of intent.

IM Pei’s modern complement to the National Gallery’s neoclassical West Building originally opened in 1978. It is an impressive but stubborn structure, whose massive atrium, topped by a site-specific mobile by Alexander Calder, dominates small suites of galleries on the building’s triangular exterior. The atrium has always been great for large-scale sculpture, and works by David Smith, Isamu Noguchi and Jean Dubuffet look as good as ever there now. But the smaller galleries could feel like an afterthought. The principal exhibition spaces were on the concourse level, without natural light, while the collection galleries were disjointed.

The new, unobtrusive additions do a fair job of alleviating those shortcomings. (They were designed by the architect Perry Chin, a former associate of Pei, who is now 99 years old and long retired.) Carpet has been torn up, replaced with handsome oak floors. New diamond-shaped stairwells, kitted out in Tennessee pink marble, form the skeleton of a new circulation pattern that take you from French symbolism through to the 1970s. An escalator has been bolted on to a southern wall, and riding it may give you the uncanny feeling of being transported to Pei’s later, more famous pyramid of Paris’s Musée du Louvre. A pair of skylit, hexagonal galleries at the top of the new stairwells have an ecclesiastical feel, and offer prime spaces for one-artist showcases; one is now given over to dozens of spiffy Calders.

Mel Bochner, Language Is Not Transparent, 1970 Photograph: Los Angeles County Museum of Art/Modern and Contemporary Art Council Fund

The most alluring addition is a new roof terrace, with a view of the Canadian embassy and a couple of courthouses, and the National Gallery is inaugurating it with a truly great sculpture: Katharina Fritsch’s giant blue cock, spreading its glorious plumage over the nation’s capital. (It is on long-term loan from Glenstone, one of several private museums whose tax-exempt status was recently probed by the Senate finance committee.) The German artist’s Hahn/Cock first touched down on the fourth plinth of London’s Trafalgar Square in 2013, where the rooster’s cartoon arrogance – and implicit Bonapartism: the cock is a French national symbol – poked fun at the square’s British military tributes. Up close, standing on the floor and with no obtrusive barriers, Fritsch’s cock looks even better. Its surface of matte ultramarine, as deep and glorious as the cloak of the Virgin, sucks in the light of day, and its expansive tail feathers bloom spectacularly when seen from directly below. Fritsch’s exploration of how digital fabrication both disrupts and revivifies the tradition of monumental sculpture makes her bird one of the most important artworks of our time, though it’s also a prime selfie backdrop. They will be some of the rare cock shots to make it past Instagram’s censors.

The reopened East Building also integrates new holdings accessioned from the defunct Corcoran Art Gallery, Washington’s first art museum, which closed two years ago after long stretches of mismanagement. The National Gallery has taken ownership of more than 8,000 works of art from the Corcoran, and here you’ll find such adopted artworks as Terry Winters’s Theophrastus Garden II (1982): an all-over wash of brown and bronze studded with circular explosions that might as well be paintballs, large enough to hold its own in the oversized atrium. Elsewhere the Corcoran acquisitions form part of a refreshed permanent collection hang, with particular strengths in minimal and conceptual art, plus luscious paintings from Washington painters, among them Morris Louis and Sam Gilliam. Sure, it could use some more diversity and much more art from beyond the US and western Europe. But it’s an honest presentation of a collection with strengths and weaknesses, and who goes to the National Gallery for experiment?

Three temporary exhibitions inaugurate the new East Building: two missable, one major. There’s a small takeover of a tower gallery by the verbose Barbara Kruger, plus a soporific, by-the-numbers showcase of the most auction-approved names of contemporary photography. By far the most important, and most impressive, is Los Angeles to New York: Dwan Gallery, 1959–1971, which is both a shrewd study of 60s art history and a celebration of a major gift to the museum. (Next year the show, curated by James Meyer, will travel to the Los Angeles County Museum of Art.)

The bicoastal Dwan Gallery mounted one of the earliest exhibitions of pop art, in 1962. It showed Andy Warhol’s Brillo boxes for the first time in 1964. Later its founder, Virginia Dwan, became a Medici of the desert, funding such giant earthworks as Robert Smithson’s Spiral Jetty and Charles Ross’s Star Axis. Though the artists she showed have coalesced into a sort of post-Pollock Greatest Generation – think Robert Rauschenberg, Claes Oldenburg, Dan Flavin, Sol LeWitt – they were far from commercial successes at the time, and Dwan Gallery closed after 12 years. But the dealer’s weighty collection, much of it first shown in her galleries or created by her friends, has now entered the American national collection: 250 paintings, sculptures, artists’ books and other relics from an age of American cultural dominance.

Dwan also had a marked interest in French art of the 1960s, and the National Gallery show includes important works by Yves Klein, Martial Raysse and other artists of nouveau réalisme. But her collection testifies to a moment when artists in the US – for better, for worse – decided they had no more need of Europe and created a language of their own. Dozens of languages, actually. LeWitt’s iterative grid of white towers, Carl Andre’s unshowy typewritten poetry, Smithson’s spiral in a salt lake, Ed Kienholz’s full-scale diorama of rutting teenagers – they have little in common in formal terms, but together they limn an era of American change and conflict, pride and anxiety. Any museum would be lucky to have this gift. It seems right, though, it has landed in a national gallery, to be wrestled with by Americans still making out what this country means.

This article was amended on 7 October 2016 to clarify the nature of the Senate finance committee investigation into private museums.